THE PARAMETER KERNELS FOR THE LINEAR INVERSION OF THE FREE OSCILLATION OF THE EARTH (Ⅰ)

In the linear inversion of the radial variation of the parameters of the Earth by usingthe observed frequencies of various normal modes of free oscillation of the earth, it is neces-sary to know the values of the kernels of the parameters ρ, μ and λ. This paper describesthe methods of the derivation of the formulas of these kernels. This is the first part of thepaper in which only the toroidal oscillations are considered. They are much simpler thanthose of the spheroidal ones, that we will consider in the second part of the paper. The data of the two types of oscillations are equally important in the solution of theinversion problem, and should be employed simultaneously, and we know that the toroidaloscillations are much simpler than the spheroidal ones, it seems wise to divide the whole programof the inversion problem into steps: first, by employing the toroidal data to correct the twoparameters ρ and μ in the mantle, then by using the spheroidal data to correct the remain-ing parameters, i.e. th